Turbulent convection in rapidly rotating spherical shells: A model for equatorial and high latitude jets on Jupiter and Saturn

The origin of zonal jets on the jovian planets has long been a topic of scientific debate. In this paper we show that deep convection in a spherical shell can generate zonal flow comparable to that observed on Jupiter and Saturn, including a broad prograde equatorial jet and multiple alternating jets at higher latitudes. We present fully turbulent, 3D spherical numerical simulations of rapidly rotating convection with different spherical shell geometries. The resulting global flow fields tend to be segregated into three regions (north, equatorial, and south), bounded by the tangent cylinder that circumscribes the inner boundary equator. In all of our simulations a strong prograde equatorial jet forms outside the tangent cylinder, whereas multiple jets form in the northern and southern hemispheres, inside the tangent cylinder. The jet scaling of our numerical models and of Jupiter and Saturn is consistent with the theory of geostrophic turbulence, which we extend to include the effect of spherical shell geometry. Zonal flow in a spherical shell is distinguished from that in a full sphere or a shallow layer by the effect of the tangent cylinder, which marks a reversal in the sign of the planetary β-parameter and a jump in the Rhines length. This jump is manifest in the numerical simulations as a sharp equatorward increase in jet widths—a transition that is also observed on Jupiter and Saturn. The location of this transition gives an estimate of the depth of zonal flow, which seems to be consistent with current models of the jovian and saturnian interiors.     

Compressible convection in the deep atmospheres of giant planets

Fast rotating giant planets such as Jupiter and Saturn possess alternate prograde and retrograde zonal winds which are stable over long periods of time. We consider a compressible model of convection in a spherical shell with rapid rotation, using the anelastic approximation, to explore the parameter range for which such zonal flows can be produced.We consider models with a large variation in density across the layer. Our models are based only on the molecular H/He region above the metallic hydrogen transition at about 2 Mbar, and we do not include the hydromagnetic effects which may be important if the electrical conductivity is significant. We find that the convective velocities are significantly higher in the low density regions of the shell, but the zonal flow is almost independent of the z-coordinate parallel to the rotation axis. We analyse how this behaviour is consistent with the Proudman-Taylor theorem.We find that deep prograde zonal flow near the equator is a very robust feature of our models. Prograde and retrograde jets alternating in latitude can occur inside the tangent cylinder in compressible as well as Boussinesq models, particularly at lower Prandtl numbers. However, the zonal jets inside the tangent cylinder are suppressed if a no-slip condition is imposed at the inner boundary. This suggests that deep high latitude jets may be suppressed if there is significant magnetic dissipation.Our compressible calculations include the viscous dissipation in the entropy equation, and we find this is comparable to, and in some cases exceeds, the total heat flux emerging from the surface. For numerical reasons, these simulations cannot reach the extremely low Ekman number found in giant planets, and they necessarily also have a much larger heat flux than planets. We therefore discuss how our results might scale down to give solutions with lower dissipation and lower heat flux.     

Zonal jets in rotating convection with mixed mechanical boundary conditions

Large-scale zonal flows, as observed on the giant planets, can be driven by thermal convection in a rapidly rotating spherical shell. Most previous models of convectively-driven zonal flow generation have utilized stress-free mechanical boundary conditions (FBC) for both the inner and the outer surfaces of the convecting layer. Here, using 3D numerical models, we compare the FBC case to the case with a stress free outer boundary and a non-slip inner boundary, which we call the mixed case (MBC). We find significant differences in surface zonal flow profiles produced by the two cases. In low to moderate Rayleigh number FBC cases, the main equatorial jet is flanked by a strong, high-latitude retrograde jets in the northern and southern hemispheres. For the highest Rayleigh number FBC case, the equatorial jet is flanked by strong reversed jets as well as two additional large-scale alternating jets at higher latitudes. The MBC cases feature stronger equatorial jets but, much weaker, small-scale alternating zonal flows are found at higher latitudes. Our high Rayleigh number FBC results best compare with the zonal flow pattern observed on Jupiter, where the equatorial jet is flanked by strong retrograde jets as well as small-scale alternating jets at high latitude. In contrast, the MBC results compare better with the observed flow pattern on Saturn, which is characterized by a dominant prograde equatorial jet and a lack of strong high latitude retrograde flow. This may suggest that the mechanical coupling at the base of the jovian convection zone differs from that on Saturn.     

A dynamo driven by zonal jets at the upper surface: Applications to giant planets

We present a dynamo mechanism arising from the presence of barotropically unstable zonal jet currents in a rotating spherical shell. The shear instability of the zonal flow develops in the form of a global Rossby mode, whose azimuthal wavenumber depends on the width of the zonal jets. We obtain self-sustained magnetic fields at magnetic Reynolds numbers greater than 10³. We show that the propagation of the Rossby waves is crucial for dynamo action. The amplitude of the axisymmetric poloidal magnetic field depends on the wavenumber of the Rossby mode, and hence on the width of the zonal jets. We discuss the plausibility of this dynamo mechanism for generating the magnetic field of the giant planets. Our results suggest a possible link between the topology of the magnetic field and the profile of the zonal winds observed at the surface of the giant planets. For narrow Jupiter-like jets, the poloidal magnetic field is dominated by an axial dipole whereas for wide Neptune-like jets, the axisymmetric poloidal field is weak.     

Subcritical dynamos in shear flows

Identifying generic physical mechanisms responsible for the generation of magnetic fields and turbulence in differentially rotating flows is fundamental to understand the dynamics of astrophysical objects such as accretion disks and stars. In this paper, we discuss the concept of subcritical dynamo action and its hydrodynamic analogue exemplified by the process of nonlinear transition to turbulence in non‐rotating wall‐bounded shear flows. To illustrate this idea, we describe some recent results on nonlinear hydrodynamic transition to turbulence and nonlinear dynamo action in rotating shear flows pertaining to the problem of turbulent angular momentum transport in accretion disks. We argue that this concept is very generic and should be applicable to many astrophysical problems involving a shear flow and non‐axisymmetric instabilities of shearinduced axisymmetric toroidal velocity or magnetic fields, such as Kelvin‐Helmholtz, magnetorotational, Tayler or global magnetoshear instabilities. In the light of several recent numerical results, we finally suggest that, similarly to a standard linear instability, subcritical MHD dynamo processes in high‐Reynolds number shear flows could act as a large‐scale driving mechanism of turbulent flows that would in turn generate an independent small‐scale dynamo. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Large-scale zonal flow and magnetic field generation due to drift-Alfven turbulence in ionosphere plasma

In the present work, the generation of large-scale zonal flows and magnetic field by short-scale collision-less electron skin depth order drift-Alfven turbulence in the ionosphere is investigated. The self-consistent system of two model nonlinear equations, describing the dynamics of wave structures with characteristic scales till to the skin value, is obtained. Evolution equations for the shear flows and the magnetic field is obtained by means of the averaging of model equations for the fast-high-frequency and small-scale fluctuations. It is shown that the large-scale disturbances of plasma motion and magnetic field are spontaneously generated by small-scale drift-Alfven wave turbulence through the nonlinear action of the stresses of Reynolds and Maxwell. Positive feedback in the system is achieved via modulation of the skin size drift-Alfven waves by the large-scale zonal flow and/or by the excited large-scale magnetic field. As a result, the propagation of small-scale wave packets in the ionospheric medium is accompanied by low-frequency, long-wave disturbances generated by parametric instability. Two regimes of this instability, resonance kinetic and hydrodynamic ones, are studied. The increments of the corresponding instabilities are also found. The conditions for the instability development and possibility of the generation of large-scale structures are determined. The nonlinear increment of this interaction substantially depends on the wave vector of Alfven pumping and on the characteristic scale of the generated zonal structures. This means that the instability pumps the energy of primarily small-scale Alfven waves into that of the large-scale zonal structures which is typical for an inverse turbulent cascade. The increment of energy pumping into the large-scale region noticeably depends also on the width of the pumping wave spectrum and with an increase of the width of the initial wave spectrum the instability can be suppressed. It is assumed that the investigated mechanism can refer directly to the generation of mean flow in the atmosphere of the rotating planets and the magnetized plasma.     

Kinematics of the active region of the quasar 3C 345

The fine structure of the quasar 3C 345 in polarized emission at 7 mm and 2 cm has been investigated. The kinematics is shown to correspond to an anticentrifuge: the thermal plasma of the surrounding space accretes onto the disk, flows to the center, and is ejected in the form of a rotating bipolar outflow that carries away the excess angular momentum as it accumulates. The bipolar outflow consists of a high-velocity central jet surrounded by a low-velocity component. The low-velocity flows are the rotating hollow tubes ejected from the peripheral part of the disk with a diameter ～Ø₁ = 2.2 pc and from the region Ø₂ = 1 pc. The high-velocity jet with a diameter Ø₃ = 0.2 pc is ejected from the central part of the disk, while the remnant falls onto the forming central body. The ejection velocity of the high-velocity flow is v ? 0.06c. At a distance up to ～1 pc, the jet accelerates to an apparent velocity v ～ 8c. Further out, uniform motion is observed within ～2 pc following which deceleration occurs. The jet structure corresponding to a conical diverging helix with an increasing pitch is determined by gasdynamic instability. The counterjet structure is a mirror reflection of the nearby part of the jet. The brightness temperature of the fragment of the high-velocity flow at the exit from the counterjet nozzle is T _b ≈ (10¹²?10¹³) K. The disk inclined at an angle of 60° to the plane of the sky shadows the jet ejector region. Ring currents observed in the tangential directions as parallel chains of components are excited in the rotating flows. The magnetic fields of the rotating bipolar outflow and the disk are aligned and oriented along the rotation axis. The translational motions of the jet and counterjet are parallel and antiparallel to the magnetic field, which determines their acceleration or deceleration. The quasar core is surrounded by a thermal plasma. The sizes of the HII region reach ～30 pc. The electron density decreases with increasing distance from the center from N _e ≈ 10⁸ to ≈10⁵ cm^?3. The observed emission from the jet fragments at the exit from the nozzle is partially absorbed by the thermal plasma, is refracted with increasing distance—moves with an apparent superluminal velocity, and decelerates as it goes outside the HII region.     

Effects of compressibility on driving zonal flow in gas giants

The banded structures observed on the surfaces of the gas giants are associated with strong zonal winds alternating in direction with latitude. We use three-dimensional numerical simulations of compressible convection in the anelastic approximation to explore the properties of zonal winds in rapidly rotating spherical shells. Since the model is restricted to the electrically insulating outer envelope, we therefore neglect magnetic effects.A systematic parametric study for various density scaleheights and Rayleigh numbers allows to explore the dependence of convection and zonal jets on these parameters and to derive scaling laws.While the density stratification affects the local flow amplitude and the convective scales, global quantities and zonal jets properties remain fairly independent of the density stratification. The zonal jets are maintained by Reynolds stresses, which rely on the correlation between zonal and cylindrically radial flow components. The gradual loss of this correlation with increasing supercriticality hampers all our simulations and explains why the additional compressional source of vorticity hardly affects zonal flows.All these common features may explain why previous Boussinesq models were already successful in reproducing the morphology of zonal jets in gas giants.     

On the multiple jet flows in Jupiter''s atmosphere

Measurements by the Galileo probe in Jupiter's deep atmosphere support the possibility that the mean zonal multiple-jet flows in Jupiter's atmosphere are deep rooted. As a consequence of Jupiter's high rotation rate, the primary dynamics of the zonal flows must be geostrophic, i.e., the dynamic balance is largely between the Coriolis and pressure forces. This paper describes a new analytical theory for the generation of zonal multiple-jet flows on the basis of the nonlinear interaction of slowly traveling, nearly two-dimensional and non-axisymmetric geostrophic waves. An explicit analytical expression for the geostrophic waves is obtained as the leading-order solution of the weakly nonlinear problem. In the high-order problem taking into account of nonlinear effects, an analytical expression for an alternating multiple-jet flow is derived. Implications of the theory for Jupiter and other planets are discussed.     

木星大气中交替快速环流研究

伽利略探测器对木星深部的大气测量，进一步增加了木星大气的平均带状交替快速环流是由其深部大气运动产生的可能性。由于木星高速自转，所以此带状流的基本动力学特征是地转流，即主要动力学平衡是科里奥利力和压力。基于近两维和非轴对称地转慢波的非线性相互作用，描述了一个新的带状交替环流的分析理论，并给出了地转波动的一个显函数关系分析表达式，以及它对应于弱非线性问题的首阶解。对考虑非线性效应的高阶解问题，推导出了一个运动方向交替的快速环流的分析表达式。也对该理论在木星和其他行星的大气动力学研究方面作了讨论。     

Radiative instability of a cloudy planetary atmosphere

A cloudy planetary atmosphere at rest is shown to be unstable to disturbances of large horizontal scale. The energy source for the instability is the change in radiative heat flux associated with vertical displacement near the emitting level. A simple model is described in which Q∞ δz, where Q is the net heating rate in the cloud and δz is vertical displacement. The constant of proportionality may be either positive or negative. Disturbances may take the form of either quasi-steady geostrophic motions or amplified inertia-gravity waves. The model is applied to Jupiter's zonal winds and to motions near the Venus cloud tops, and provides a possible explanation for many important features of these two flows.     

Emergence of polar-jet polygons from jet instabilities in a Saturn model

Voyager flybys of Saturn in 1980-1981 revealed a circumpolar wave at ≈78° north planetographic latitude. The feature had a dominant wavenumber 6 mode, and has been termed the Hexagon from its geometric appearance in polar-projected mosaics. It was also noted for being stationary with respect to Saturn’s Kilometric Radiation (SKR) rotation rate. The Hexagon has persisted for over 30 years since the Voyager observations until now. It has been observed from ground based telescopes, Hubble Space Telescope and multiple instruments onboard Cassini in orbit around Saturn. Measurements of cloud motions in the region reveal the presence of a jet stream whose path closely follows the Hexagon’s outline. Why the jet stream takes the characteristic six-sided shape and how it is stably maintained across multiple saturnian seasons are yet to be explained. We present numerical simulations of the 78.3°N jet using the Explicit Planetary Isentropic-Coordinate (EPIC) model and demonstrate that a stable hexagonal structure can emerge without forcing when dynamic instabilities in the zonal jet nonlinearly equilibrate. For a given amplitude of the jet, the dominant zonal wavenumber is most strongly dependent on the peak curvature of the jet, i.e., the second north-south spatial derivative of the zonal wind profile at the center of the jet. The stable polygonal shape of the jet in our simulations is formed by a vortex street with cyclonic and anticyclonic vortices lining up towards the polar and equatorial side of the jet, respectively. Our result is analogous to laboratory experiments of fluid motions in rotating tanks that develop polygonal flows out of vortex streets. However, our results also show that a vortex street model of the Hexagon cannot reproduce the observed propagation speed unless the zonal jet’s speed is modified beyond the uncertainties in the observed zonal wind speed, which suggests that a vortex street model of the Hexagon and the observed zonal wind profile may not be mutually compatible.     

Simulating Magnetized Jets

A suitable model for the macroscopic behavior of accretion disk-jet systems is provided by the equations of MagnetoHydroDynamics (MHD). These equations allow us to perform scale-encompassing numerical simulations of multidimensional nonlinear magnetized plasma flows. For that purpose, we continue the development and exploitation of the Versatile Advection Code (VAC) along with its recent extension which employs dynamically controlled grid adaptation. In the adaptive mesh refinement AMRVAC code, modules for simulating any-dimensional special relativistic hydro- and magnetohydrodynamic problems are currently operational. Here, we review recent 3D MHD simulations of fundamental plasma instabilities, relevant when dealing with cospatial shear flow and twisted magnetic fields. Such magnetized jet flows can be susceptible to a wide variety of hydro (e.g. Kelvin-Helmholtz) or magnetohydrodynamic (e.g. current driven kink) instabilities. Recent MHD computations of 3D jet flows have revealed how such mutually interacting instabilities can in fact aid in maintaining jet coherency. Another breakthrough from computational magnetofluid modeling is the demonstration of continuous, collimated, transmagnetosonic jet launching from magnetized accretion disks. Summarizing, MHD simulations are rapidly gaining realism and significantly advance our understanding of nonlinear astrophysical magnetofluid dynamics.     

Deep jets on gas-giant planets

Three-dimensional numerical simulations of the atmospheric flow on giant planets using the primitive equations show that shallow thermal forcing confined to pressures near the cloud tops can produce deep zonal winds from the tropopause all the way down to the bottom of the atmosphere. These deep winds can attain speeds comparable to the zonal jet speeds within the shallow, forced layer; they are pumped by Coriolis acceleration acting on a deep meridional circulation driven by the shallow-layer eddies. In the forced layer, the flow reaches an approximate steady state where east-west eddy accelerations balance Coriolis accelerations acting on the meridional flow. Under Jupiter-like conditions, our simulations produce 25 to 30 zonal jets, similar to the number of jets observed on Jupiter and Saturn. The simulated jet widths correspond to the Rhines scale; this suggests that, despite the three-dimensional nature of the dynamics, the baroclinic eddies energize a quasi-two-dimensional inverse cascade modified by the β effect (where β is the gradient of the Coriolis parameter). In agreement with Jupiter, the jets can violate the barotropic and Charney-Stern stability criteria, achieving curvatures ^∂2u/∂y² of the zonal wind u with northward distance y up to 2β. The simulations exhibit a tendency toward neutral stability with respect to Arnol'd's second stability theorem in the upper troposphere, as has been suggested for Jupiter, although deviations from neutrality exist. When the temperature varies strongly with latitude near the equator, our simulations can also reproduce the stable equatorial superrotation with wind speeds greater than . Diagnostics show that barotropic eddies at low latitudes drive the equatorial superrotation. The simulations also broadly explain the distribution of jet-pumping eddies observed on Jupiter and Saturn. While idealized, these simulations therefore capture many aspects of the cloud-level flows on Jupiter and Saturn.     

The instability of hydromagnetic planetary-gravity waves in a zonal flow and transverse magnetic field

Hydromagnetic planetary-gravity waves propagating on a β-plane through a zonal flow and transverse magnetic field are examined for instability. Such instabilities may be related to same physical phenomena in the atmospheres of the Sun and planets and in the Earth's core. It is found that the onset of instability depends on the directions of the vertical and transverse wave-numbers and the zonal flow. It is also shown that as the magnetic field intensity is kept uniform instability can onset provided that the zonal flow strength does not exceed a certain factor, which depends on the parameters of the medium, and then the zonal wavenumbers that can become unstable are limited to a given range. If the basic Alfvén wave speed is allowed to vary whereas the zonal flow is kept uniform the zonal wavenumbers that can exhibit instability are again limited but the basic Alfvén wave speed can assume any value.     

Shear flow instabilities in rotating systems

An asymptotic approach is developed for examining the linear stability of a plane-parallel shear flow in a rotating system with respect to long wave disturbances for a general velocity profile. Formulas for the determination of the instability characteristics are obtained and solved numerically in the case of hyperbolic tangent profile.     

Parker instability in a self-gravitating magnetized gas disk: II. Competition between gravitational and convective instabilities

Under influence of external gravity generated by Galactic all components excluding ISM, a magnetized gas disk may experience both Parker and convective instabilities. Growth rate of the convective instability increases with decreasing perturbation wavelength, and the convective motion makes sheet-like structures all over before the Parker instability forms structures of any meaningful size in the disk. Yet the Parker instability is thought to be an ideal route to form large-scale condensations in the Galaxy. In search of a means to curb convective activities in the Galactic ISM disk, the external gravity is replaced by self-gravity as a driving force of the Parker instability and the gravitational instability is invoked to reinforce the Parker instability. Perturbation of interchange mode is known to trigger convective instability in such disk and the one of undular mode to activate the Parker instability, while the gravitational instability can be triggered by both modes. Therefore, the resulting Jeans instability would help the Parker instability to overcome disrupting behavior of the convection. Dynamical properties of the disk can be characterized by ratio α of magnetic to gas pressure, adiabatic exponent γ, scale height H of the ISM, and disk thickness z_a. A linear stability analysis has been done to the disk, and the maximum growth rate of the Parker–Jeans instability is compared with that of the convective instability. The latter may or may not be higher than the former, depending on the disk parameters. The Parker–Jeans instability has chances to override the convective instability, when the disk is thicker than a certain value. In the disk thinner than the critical one, the Jeans instability can always suppress the convection. Since the growth rate of the convective instability is proportional to local gravitational acceleration, thereby in the general Galactic gravity, the convective instability works actively only in upper regions, we expect chaotic features to appear in regions of low density far from Galactic mid-plane.     

Dynamical properties of the Venus mesosphere from the radio-occultation experiment VeRa onboard Venus Express

The dynamics of Venus’ mesosphere (60–100 km altitude) was investigated using data acquired by the radio-occultation experiment VeRa on board Venus Express. VeRa provides vertical profiles of density, temperature and pressure between 40 and 90 km of altitude with a vertical resolution of few hundred meters of both the Northern and Southern hemisphere. Pressure and temperature vertical profiles were used to derive zonal winds by applying an approximation of the Navier–Stokes equation, the cyclostrophic balance, which applies well on slowly rotating planets with fast zonal winds, like Venus and Titan. The main features of the retrieved winds are a midlatitude jet with a maximum speed up to 140 ± 15 m s^?1 which extends between 20°S and 50°S latitude at 70 km altitude and a decrease of wind speed with increasing height above the jet. Cyclostrophic winds show satisfactory agreement with the cloud-tracked winds derived from the Venus Monitoring Camera (VMC/VEx) UV images, although a disagreement is observed at the equator and near the pole due to the breakdown of the cyclostrophic approximation. Knowledge of both temperature and wind fields allowed us to study the stability of the atmosphere with respect to convection and turbulence. The Richardson number Ri was evaluated from zonal field of measured temperatures and thermal winds. The atmosphere is characterised by a low value of Richardson number from ～45 km up to ～60 km altitude at all latitudes that corresponds to the lower and middle cloud layer indicating an almost adiabatic atmosphere. A high value of Richardson number was found in the region of the midlatitude jet indicating a highly stable atmosphere. The necessary condition for barotropic instability was verified: it is satisfied on the poleward side of the midlatitude jet, indicating the possible presence of wave instability.     

The effects of vigorous mixing in a convective model of zonal flow on the ice giants

Previous studies have used models of three-dimensional (3D) Boussinesq convection in a rotating spherical shell to explain the zonal flows on the gas giants, Jupiter and Saturn. In this paper we demonstrate that this approach can also generate flow patterns similar to those observed on the ice giants, Uranus and Neptune. The equatorial jets of Uranus and Neptune are often assumed to result from baroclinic cloud layer processes and have been simulated with shallow layer models. Here we show that vigorous, 3D convection in a spherical shell can produce the retrograde (westward) equatorial flows that occur on the ice giants as well as the prograde (eastward) equatorial flows of the gas giants. In our models, the direction of the equatorial jet depends on the ratio of buoyancy to Coriolis forces in the system. In cases where Coriolis forces dominate buoyancy, cylindrical Reynolds stresses drive prograde equatorial jets. However, as buoyancy forces approach and exceed Coriolis forces, the cylindrical nature of the flow is lost and 3D mixing homogenizes the fluid's angular momentum; the equatorial jet reverses direction, while strong prograde jets form in the polar regions. Although the results suggest that conditions involving strong atmospheric mixing are responsible for generating the zonal flows on the ice giants, our present models require roughly 100 and 10 times the internal heat fluxes observed on Uranus and Neptune, respectively.     

Interaction between sheared flow and resistive tearing mode

We investigate the nonlinear evolution of resistive tearing mode in a current sheet with a sheared flow in a long, thin cylinder. The results show that a hyperbolic secant (sech) flow field will lead to instability of the resistive tearing mode, formation of magnetic islands and rapid release of magnetic energy. The coupling between sheared flow and the tearing mode and interaction between suprathermal instabilities change the degree of shear in the magnetic field (the electric current gradient) and drive the development of the instability. This process may be one of the mechanisms of solar flares.